On global solutions to a defocusing semi-linear wave equation

Abstract

We prove that the 3D cubic defocusing semi-linear wave equation is globally well-posed for data in the Sobolev space ${\dot{H}}^s$ where $s>3/4$. This result was obtained in [Kenig-Ponce-Vega, 2000] following Bourgain's method ([Bourgain, 1998]). We present here a different and somewhat simpler argument, inspired by previous work on the Navier-Stokes equations ([Calderon, 1990], [Gallagher-Planchon, 2002]).